共查询到20条相似文献,搜索用时 15 毫秒
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This paper contains some theorems related to the best approximation ρn(f;E) to a function f in the uniform metric on a compact set by rational functions of degree at most n. We obtain results characterizing the relationship between ρn(f;K) and ρn(f;E) in the case when complements of compact sets K and E are connected, K is a subset of the interior Ω of E, and f is analytic in Ω and continuous on E. 相似文献
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We explicitly determine the best uniform polynomial approximation to a class of rational functions of the form 1/2(x−c)+K(a,b,c,n)/(x−c) on [a,b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n−1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle η in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions. 相似文献
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On approximation to an analytic function by rational functions of best approximation 总被引:1,自引:0,他引:1
J. L. Walsh 《Mathematische Zeitschrift》1934,38(1):163-176
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() [0,1] — {(n)} — , +. , f(x) [0,1]
() , x
1
,x
2 [0, 1], (1)=(2), f(x
1
)=f(x
2
). 相似文献
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We study the asymptotic behavior of the rate of convergence of Dirichlet series that are absolutely convergent in a half-plane;
the results obtained are applicable to rational approximation of functions analytic in the unit disk with nonnegative Taylor
coefficients.
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 116–122. 相似文献
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V. V. Maimeskul 《Ukrainian Mathematical Journal》1993,45(11):1713-1726
Upper and lower bounds are established for the rate of rational approximation of functions piecewise analytic on tangent continua. In some special cases, these bounds are coordinated depending on the mutual location of the continua.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 11, pp. 1522–1533, November, 1993. 相似文献
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R. R. Akopyan 《Proceedings of the Steklov Institute of Mathematics》2015,288(1):5-12
On the class of functions analytic in a strip, we study a number of related extremal problems for the differentiation operator: the best approximation of the operator, computation of its modulus of continuity, and optimal recovery of the operator from boundary values of a function given with error on a straight line. 相似文献
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The paper provides an overview of the author’s contribution to the theory of constructive rational approximations of analytic functions. The results presented are related to the convergence theory of Padé approximants and of more general rational interpolation processes, which significantly expand the classical theory’s framework of continuous fractions, to inverse problems in the theory of Padé approximants, to the application of multipoint Padé approximants (solutions of Cauchy-Jacobi interpolation problem) in explorations connected with the rate of Chebyshev rational approximation of analytic functions and to the asymptotic properties of Padé-Hermite approximation for systems of Markov type functions. 相似文献
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V. R. Kravchuk 《Ukrainian Mathematical Journal》1992,44(7):903-905
It is shown that it is possible to apply a method proposed by V. K. Dzyadyk for the construction of rational functions that realize a near optimal approximation of entire elementary functions. The method may be termed linear in the sense that all the coefficients of the rational functions are determined from two systems of linear algebraic equations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 7, pp. 998–1000, July, 1992. 相似文献
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B. D. Boyanov 《Mathematical Notes》1973,14(1):551-556
The author considers a class F of analytic functions real in the interval [-1, 1] and bounded in the unit circle. As an estimate of the optimal quadrature error R(n) over the class F it is shown that $$_e - \left( {2\sqrt 2 + \frac{1}{{\sqrt 2 }}} \right)\pi \sqrt n \leqslant R(n) \leqslant e^{ - \frac{\pi }{{\sqrt 2 }}n} .$$ With the additional condition that \(\mathop {max}\limits_{x \in [ - 1,1]}\) ¦f(x)¦?B, an estimate is obtained for the ?-entropy H?(F): $$\frac{8}{{27}}\frac{{(1n2)^2 }}{{\pi ^2 }} \leqslant \mathop {\lim }\limits_{\varepsilon \to 0} \frac{{H_\varepsilon (F)}}{{\left( {\log \frac{1}{\varepsilon }} \right)^3 }} \leqslant \frac{2}{{\pi ^2 }}(1n2)^2 .$$ 相似文献
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We construct a new scheme of approximation of any multivalued algebraic function f(z) by a sequence {rn(z)}n∈N of rational functions. The latter sequence is generated by a recurrence relation which is completely determined by the algebraic equation satisfied by f(z). Compared to the usual Padé approximation our scheme has a number of advantages, such as simple computational procedures that allow us to prove natural analogs of the Padé Conjecture and Nuttall's Conjecture for the sequence {rn(z)}n∈N in the complement CP1?Df, where Df is the union of a finite number of segments of real algebraic curves and finitely many isolated points. In particular, our construction makes it possible to control the behavior of spurious poles and to describe the asymptotic ratio distribution of the family {rn(z)}n∈N. As an application we settle the so-called 3-conjecture of Egecioglu et al. dealing with a 4-term recursion related to a polynomial Riemann Hypothesis. 相似文献
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Gaetano Fichera 《Annali di Matematica Pura ed Applicata》1970,84(1):375-386
Summary Viene data la condizione necessaria e sufficiente perchè le funzioni razionali di una variabile, aventi poli di ordine prefissato
in assegnati punti del piano complesso, costituiscano un sistema completo iu Co (0, 1).
A Bruno Finzi nel suo70
mo
compleanno.
This research has been sponsored in part by the Aerospace Research Laboratoires through the European Office of Aerospace Research,
OAR, United States Air Force, under Grant EOOAR-69-0066.
Entrata in Redazione il 22 aprile 1970. 相似文献
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李书海 《纯粹数学与应用数学》2005,21(1):73-75
引进用Hλ算子定义的一类解析函数Pλ(μ,α,β).我们导出该类中函数的积分表达式,证明偏差定理,并推广了文[3]中的主要结果.同时改进了[4]中的一个不等式. 相似文献
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